Simplify (2x)^(1/3)*(2x)^(4/3)

${(2 x)}^{\frac{1}{3}} \cdot {(2 x)}^{\frac{4}{3}}$

Multiply ${(2 x)}^{\frac{1}{3}}$ by ${(2 x)}^{\frac{4}{3}}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(2 x)}^{\frac{1}{3} + \frac{4}{3}}$

Combine the numerators over the common denominator.

${(2 x)}^{\frac{1 + 4}{3}}$

Add $1$ and $4$ .

${(2 x)}^{\frac{5}{3}}$

Apply the product rule to $2 x$ .

$2^{\frac{5}{3}} x^{\frac{5}{3}}$